Hello and welcome to JustAnswer!
When this happens are the gauges on the dash working, or are they down? (this is very important)
So at least part of the instrument cluster is down then, I'd bet the gauges probably aren't working at that time either.
The printed circuit board on the back of the instrument cluster itself gives a bit of problems on these vans. That's where I would expect your problem to be. A quick fix, when it's acting up, turn the key on and give the dash a decent smack right over the top of the cluster. If it comes back on you know that's where the problem is. This may ore may not help though.
What happens is when the cluster goes down it will short the communication bus system to a higher voltage and it stops all of the modules on the van from communicating with each other. Your factory security is controlled by the body control module. It has to send a signal over the bus to the engine controller that the system has been disarmed and it's ok to start the engine. When the bus is down the controllers can't talk and the engine controller assumes you are stealing the van. It starts up, runs for 2 seconds, and shuts the fuel injectors off.
If the circuit board is the problem there are a few choices. You could have the board replaced. It runs between $4-500 plus calibration. You can also normally pick up a whole used cluster at a salvage yard for about $100, install it and have it calibrated. If you're handy with a soldering iron you may be able to fix the old one yourself. There is a problem area on the boards where the electrical connector terminals solder to the circuit board. If you pull the board off the cluster and look at the other side you will see the solder joints. With a magnifying glass or microscope check out these joints for cracks. You may find these solder joints are cracked and causing the problem. You may be able to see the cracks with a naked eye, and you might not. Either way, carefully resolder the joints and see if it helps. Most of the time this will fix the problem, and it's a free repair you can do without expensive part replacement.